“I never thought I’d be a dad, until I got sober,” the longtime musician and dad to 4-month-old daughter Liliana Carella tells PEOPLE. “Then my life really started to take shape.”

Rzeznik recalls, “Somebody told me that kids force you to become the person you should have been all along,” sharing that from the moment his baby girl came into the world, he felt that corresponding mental shift.

“When I held Lili for the first time and saw her being born, the first thing I thought was, ‘Don’t screw this up,’ ” he says, joking, “The second thing was, ‘I gotta work — to be able to afford a kid!’ ”

Rzeznik was born and raised in Buffalo, New York — where he met bandmate and longtime friendRobby Takac — but now resides with his family in New Jersey.

And though the “Black Balloon” singer has strong Buffalo ties, he admits he feels like he’s “home for the first time” with his wife and daughter and “[loves] being a dad.”

“I had a crazy family growing up. I never felt like I was home,” he explains. “When I got sober, I became emotionally sober. It took a few months and a lot of crying. Then everything opened up and I was able to see the possibility of things, and I’m with this awesome woman who turned out to be the best friend I ever had.”

Speaking of his wife, Rzeznik praises, “Melina has always been so good for me. She’ll gently push me in a direction, but it’s always the right one.”

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The rock duo has released 11 studio albums to date, which means there’s a very expansive discography for Rzeznik to choose from if he wants to sing to his daughter. But just like during his nuptials (“We made it perfectly clear that I would not be singing at all at our wedding,” he previously told PEOPLE), the musician doesn’t tap into his own tunes when it comes to entertaining his baby girl.

“I hum to Lili. Never my songs,” he says of his daughter, whom he calls “a doll” and whose middle name, he shares, is taken from Melina’s mother’s maiden name. “Melina played my music for her before she was born. I have a really loud voice, so I don’t want to scare her.”

Music is only a small part of the way Rzeznik connects with his daughter, though. “I like to read to her,” he shares. “She’s a few months old, but she has to know who the presidents are. I’m showing her a book about the presidents. Late at night, I will watch Noam Chomsky documentaries with her. I’m so happy and grateful she’s a girl.”

Adds Melina of her husband, “He is an amazing dad. [Lili] has him wrapped around her finger. He’s very protective, very aware. He has a million parenting books [about] what to expect. I can’t wait to see what he’s going to do when she’s more alert and in her fun stage.”

For now, Rzeznik is reveling in the present, though he can’t help the natural inclination of having positive hopes for his daughter‘s future. “I want her to be independent — to be able to live in the realm of what she wants rather than what she needs,” he says. “I want her to be strong and make the right choices.”

Goo Goo Dolls’ upcoming Long Way Home Tour across the U.S. with Phillip Phillips kicks off July 14 in Mountain View, California, concluding Sept. 17 in Goldendale, Washington. And this time, the new family member will be along for the ride (at least part of the time).

“On tour this summer, my wife and Lili will be able to come out and see me a lot. Melina can telecommute,” Rzeznik explains. “Robby lives in Buffalo and has a 5-year-old girl, Hana. Hana will be Lili’s big sister [on tour]!”

The duo’s brand new EP You Should Be Happy, a follow-up to their 2016 album Boxesthat includes a remix of that album’s title track,is available now.

For more from John Rzeznik’s family life and plans for the Goo Goo Dolls’ upcoming tour, pick up the latest issue of PEOPLE, on newsstands now.